Cell structure formation in a two-dimensional density-based dislocation dynamics model

Ronghai Wu,Michael Zaiser

doi:10.1186/s41313-020-00025-x

Abstract

Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure formation, we use a minimal model for the evolution of dislocation densities under load. By considering only two slip systems in a plane strain setting, we arrive at a model which is amenable to analytical stability analysis and numerical simulation. We use this model to establish analytical stability criteria for cell structures to emerge, to investigate the dynamics of the patterning process and establish the mechanism of pattern wavelength selection. This analysis demonstrates an intimate relationship between hardening and cell structure formation, which appears as an almost inevitable corollary to dislocation dominated strain hardening. Specific mechanisms such as cross slip, by contrast, turn out to be incidental to the formation of cellular patterns.

Highlights

Plastic deformation by dislocation motion is generally associated with dislocation patterning, leading to formation of heterogeneous dislocation arrangements
In all these respects, is instructive to discuss the relations of the present 2D model with the earlier 2D model of dislocation patterning proposed by Sandfeld and Zaiser (2015)
The authors consider the evolution of dislocations on a single slip system, where the system plane is parallel to the slip plane

Summary

Introduction

Plastic deformation by dislocation motion is generally associated with dislocation patterning, leading to formation of heterogeneous dislocation arrangements. These authors consider two models which allow for dislocations of different Burgers vector in the same elementary volume, which are described by a set of densities obeying transport equations and applied to labyrinth-like patterns emerging under cyclic loading.

Results

Conclusion